This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chem 442 Fall 2010 Second Hour Exam Answers 1) (30 points) This is a perturbation theory question, similar to the perturbed H. O. one described in class. It uses explicit matrices. The Hamiltonian matrix of the unperturbed Hamiltonian is = 500 400 60 50 H thus giving five unperturbed states of energies 0, 60, 60, 400 and 500 ( in wavenumber units). The perturbation Hamiltonian is = 10 30 10 10 30 5 10 5 1 i i H , again in wavenumbers. Calculate the perturbed energies of all five states and state whether each one was changed by a first order or a second order perturbation, or both. State 1 E perturbed =  2.166666666 2nd only State 2 E perturbed = 48.5 2nd only State 3 E perturbed = 61.66666666 2nd only State 4 E perturbed = 410 1st only State 5 E perturbed = 512 both 2) (30 points) The expectation value of the energy of some Hamiltonian and some (unnormalized) trial wavefunction is d d H E = * * where d and the integration limits are appropriate to the problem. The numerator is called a Hamiltonian integral and the denominator is a normalization integral. Variational theory minimizes this to get an approximate value for the ground state energy of the system....
View Full
Document
 Spring '11
 Linda

Click to edit the document details